Overhung load on a shaft

[mfritze]

Hello,

I am working to design a shaft (non rotating) that supports a large overhung load. Attached is a schematic of the problem.

The basic idea is there is a circular shaft of diameter 'd' inside a bearing support of internal diameter 'D'. The shaft is supported a distance of 'A' and protrudes outside the support a distance of 'L', at which a load 'P' is applied. 'd' is slightly smaller than 'D' to allow the shaft to slide in and out of the housing as need be.

Any ideas on the best way to analyze this?

I am comfortable with sizing a shaft based on the expected moment, but I am unsure about what to do on sizing the support. Specifically, what does the bearing load distribution look like? I have done some analysis by assuming d=D and assuming a linear bearing reaction at the support block, but this does not take into account the clearance between shaft and support bore.

Any thoughts would be appreciated.

Thank you,

M

 

[rb1957]

the closer the fit the better ... more like a socket.

with a gap, the cylinder will 'cock' in the hole, with point loads onto the surrounding material. if you solve the deflected shape of the cylinder, i think you'll find there is contact on the LH side. this contact means that in reality the cylinder is bearing against the support, and most distributing the load. but i see the RH end as being a point load.

Quando Omni Flunkus Moritati

 

[mfritze]

Yes. That's one thing I am trying to understand better --how increased clearance raises the bearing stress. I understand the concept but can't think of a good way to quantify it.

 

[desertfox]

Hi

The only way I can think of obtaining the reactions at the edges of the supports is to consider the shaft as a beam which as been rotated at an angle inside of the support and contacts the bottom edge of the support nearest the overhung load and the top of the support at the far end.
Then calculate the reactions as point loads but now your into hertzian stress and very small contact area's.
A suggestion might be to fit a DU bearing at each end of the support and have a good clearance between the central body of the support and the shaft see link to bearings below.

http://www.ggbearings.co.uk/

Using a bearing at each will also reduce the frictional force to be overcome when trying to move the shaft axially

 

[mfritze]

Hmm. Any reason why bearings would be better than a tightly clearanced/toleranced continuous bore? Assuming axial friction is not a problem (its not moved under load), I don't see an advantage to bearings.

I like the idea of hertz contact and point loads, although the geometry of an angled cylinder contacting a housing lip seem like a problem outside the realms of established hertzian analysis.

 

[desertfox]

Hi

If you fit journal bearings at each end it saves machining long tightly toleranced bores and ultimately might save money during manufacture, in addition what's the point of machining a long tightly controlled bore when the shaft is only going to sit on the very edges of the support.
If you have a large overhung load you will need to overcome the friction at the points of contact between the shaft and support.
You haven't posted the magnitude of the overhung the load or the materials of the shaft and support but if the materials are say both steels then the friction is increased and you might encounter the components picking up or binding with each other, on the other hand the bearing material will serve to reduce friction and thus the possible problems mentioned previously.

Regards

Desertfox

 

[rb1957]

and bearings give you a much better defined loadpath into the surrounding structure

Quando Omni Flunkus Moritati

 

[Tmoose]

If I expected the support shaft to frequently slide under load I'd want the projected bearing loading (ignoring edge loading effects) to be a few hundred psi, and choose materials and lubrication (if any) accordingly. I'd make the "length of engagement" to be at least 6 shaft diameters.

2 narrow bearings could be spaced apart along the shaft to provide lengthened engagement.

http://i286.photobucket.com/albums/ll102/avro626/Forks.jpg